Numerical studies of the KP line-solitons

•Numerical simulations of KP equation with non-decaying initial data.•Study the convergence of the initial data to exact KP line-solitons.•Compare the numerical results with the KP theory for line-solitons.

The Kadomtsev–Petviashvili (KP) equation admits a class of solitary wave solutions localized along distinct rays in the xy-plane, called the line-solitons, which describe the interaction of shallow water waves on a flat surface. These wave interactions have been observed on long, flat beaches, as well as have been recreated in laboratory experiments. In this paper, the line-solitons are investigated via direct numerical simulations of the KP equation, and the interactions of the evolved solitary wave patterns are studied. The objective is to obtain greater insight into solitary wave interactions in shallow water and to determine the extent the KP equation is a good model in describing these nonlinear interactions.